{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 频率分析 (1)：从 fchk 文件得到分子频率与简正模式"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> 创建时间：2019-10-04；最后修改：2021-06-21"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在这份文档中，我们将简单地讨论从 Gaussian 生成的 formated checkpoint 文件 (fchk 或 fch 后缀名)，依据分子的 Hessian 矩阵，给出分子的振动频率与其对应的简正运动模式。\n",
    "\n",
    "我们所计算的分子是以下显然没有优化到能量最低结构的 C<sub>2</sub>O<sub>4</sub>H<sup>+</sup> 分子。之所以选择这样一个分子，是因为作者希望能正确地计算出虚频。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ":::{warning}\n",
    "\n",
    "不处于能量最低结构的分子一般来说不适合用作频率分析。此时绘制的分子光谱图从理论上是与不可能与实验相符的。\n",
    "\n",
    "这份文档尽管使用了有虚频的分子，但若要进行真正的光谱绘制，仍然需要先对分子的结构进行优化。\n",
    "\n",
    ":::"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ":::{warning}\n",
    "\n",
    "这篇文档以后有可能会作一定程度的修改。有兴趣的读者也应当参考 Gaussian 白皮书 [Vibrational Analysis in Gaussian](http://gaussian.com/wp-content/uploads/dl/vib.pdf)。\n",
    "\n",
    ":::"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "分子结构如下："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.display import Image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 2,
     "metadata": {
      "image/png": {
       "width": 250
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(filename=\"assets/mol_fig.PNG\", width=250)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "分子对应的输入卡 {download}`C2O4H.gjf`、输出文件 {download}`C2O4H.out` 与 fchk 文件 {download}`C2O4H.fchk` 在链接中可供下载。这份文档的目标将是重复输出文件中的分子频率 `Frequencies` (单位 cm<sup>-1</sup>) 与简正坐标部分；而下一份文档将会重复红外强度 `IR Inten` (单位 km/mol) 与绘制红外光谱。以下是其中一部分频率分析的输出："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                     1                      2                      3\n",
      "                     A                      A                      A\n",
      " Frequencies -- -3561.4012             -2816.7847              -111.1073\n",
      " Red. masses --     6.8911                 1.1249                14.6979\n",
      " Frc consts  --    51.4966                 5.2586                 0.1069\n",
      " IR Inten    --  9128.2276              4124.7910                 5.3095\n",
      " Raman Activ -- 90326.7283              3896.5620                15.3400\n",
      " Depolar (P) --     0.7167                 0.2640                 0.5287\n",
      " Depolar (U) --     0.8350                 0.4177                 0.6917\n",
      "  Atom  AN      X      Y      Z        X      Y      Z        X      Y      Z\n",
      "     1   6     0.54  -0.07  -0.05     0.04  -0.01   0.03    -0.02   0.16   0.01\n",
      "     2   8    -0.14   0.02   0.01    -0.03   0.03  -0.03     0.03   0.42   0.26\n",
      "     3   6    -0.28   0.10  -0.25    -0.04   0.02  -0.03    -0.01   0.10  -0.04\n",
      "     4   8     0.03  -0.04   0.08    -0.02  -0.01   0.02     0.10  -0.33  -0.34\n",
      "     5   8    -0.12  -0.03   0.09    -0.01   0.01  -0.02     0.04  -0.46  -0.20\n",
      "     6   8     0.08   0.03   0.05     0.00  -0.01   0.01    -0.14   0.19   0.31\n",
      "     7   1    -0.67  -0.18  -0.08     0.88  -0.32   0.33     0.01  -0.21  -0.18\n"
     ]
    }
   ],
   "source": [
    "with open(\"C2O4H.out\", \"r\") as f:\n",
    "    while \"and normal coordinates\" not in f.readline(): continue\n",
    "    for _ in range(17): print(f.readline()[:-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ":::{note}\n",
    "\n",
    "频率分析 (1) 文档的目的与卢天 (Sobereva) 的 `Hess2freq` 程序 [^hess2freq] 的程序基本相同，文档的编写过程也受到不少启发。\n",
    "\n",
    "但另一方面，这份文档将会解决投影整体平动和转动模式。因此，这份文档原则上应当能通过 Hessian 矩阵，给出更为接近 Gaussian 所输出的频率的结果。而任何量化软件通常都可以计算杂化 GGA 泛函级别的 Hessian，因此这份文档可以用于补足一些不进行频率分析的软件。\n",
    "\n",
    "这份文档的一个问题会是无法对直线型或说 $3N-5$ 型分子作频率分析。文档中 $3N-6$ 的 $6$ 是 hardcoded 到代码中的。\n",
    "\n",
    ":::"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ":::{note}\n",
    "\n",
    "这篇文档不使用 Einstein Summation Convention。\n",
    "\n",
    ":::"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ":::{attention}\n",
    "\n",
    "事实上，作者并不完全理解整个计算过程的原理；但这似乎是个可行的方案。\n",
    "\n",
    ":::"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 环境准备"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "下述引入的包中，\n",
    "\n",
    "* `FormchkInterface` 可以用来读取 fchk 文件的信息；文件出自 [pyxdh](https://github.com/ajz34/Py_xDH/tree/master) 项目。\n",
    "\n",
    "* 文档中我们可能会使用众多物理常数。这些由 SciPy 提供，数据来源是 CODATA 2014。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from formchk_interface import FormchkInterface\n",
    "import numpy as np\n",
    "from functools import partial\n",
    "import scipy\n",
    "\n",
    "np.set_printoptions(5, linewidth=150, suppress=True)\n",
    "np.einsum = partial(np.einsum, optimize=[\"greedy\", 1024 ** 3 * 2 / 8])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# https://docs.scipy.org/doc/scipy/reference/constants.html\n",
    "from scipy.constants import physical_constants\n",
    "\n",
    "E_h = physical_constants[\"Hartree energy\"][0]\n",
    "a_0 = physical_constants[\"Bohr radius\"][0]\n",
    "N_A = physical_constants[\"Avogadro constant\"][0]\n",
    "c_0 = physical_constants[\"speed of light in vacuum\"][0]\n",
    "e_c = physical_constants[\"elementary charge\"][0]\n",
    "e_0 = physical_constants[\"electric constant\"][0]\n",
    "mu_0 = physical_constants[\"mag. constant\"][0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "现在我们准备分子的数据：\n",
    "\n",
    "* `natm` 原子数量 $n_\\mathrm{Atom}$\n",
    "\n",
    "* `mol_weight` 原子质量 $w_A$，向量长度 $(n_\\mathrm{Atom},)$，单位 amu\n",
    "\n",
    "* `mol_coord` 原子坐标 $A_t$，矩阵大小 $(n_\\mathrm{Atom}, 3)$，单位 Bohr\n",
    "\n",
    "* `mol_hess` 坐标二阶梯度 (Hessian 矩阵) $E_\\mathrm{tot}^{A_t B_s}$，张量大小 $(n_\\mathrm{Atom}, 3, n_\\mathrm{Atom}, 3)$，单位 E<sub>h</sub> Bohr<sup>-2</sup>\n",
    "\n",
    "本文档中，$A, B$ 指代原子，$t, s$ 指代坐标分量 $x, y$ 或 $z$。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "fchk = FormchkInterface(\"C2O4H.fchk\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "mol_weight = fchk.key_to_value(\"Real atomic weights\")\n",
    "natm = mol_weight.size\n",
    "mol_coord = fchk.key_to_value(\"Current cartesian coordinates\").reshape((natm, 3))\n",
    "mol_hess = fchk.hessian()\n",
    "mol_hess = (mol_hess + mol_hess.T) / 2\n",
    "mol_hess = mol_hess.reshape((natm, 3, natm, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 包含平动、转动的频率"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这里按照 `Hess2freq` 程序的思路进行叙述。我们首先生成带原子质量权重的力常数张量 `theta`\n",
    "\n",
    "$$\n",
    "\\Theta^{A_t B_s} = E_\\mathrm{tot}^{A_t B_s} / \\sqrt{w_A w_B}\n",
    "$$\n",
    "\n",
    "但为了程序便利，我们重定义 `theta` 的维度信息为 $(3 n_\\mathrm{Atom}, 3 n_\\mathrm{Atom})$；单位是 E<sub>h</sub> Bohr<sup>-2</sup> amu<sup>-1</sup>。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta = np.einsum(\"AtBs, A, B -> AtBs\", mol_hess, 1 / np.sqrt(mol_weight), 1 / np.sqrt(mol_weight)).reshape(3 * natm, 3 * natm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "随后，我们对其进行对角化，可以立即得到原始的分子频率 `e` 与简正坐标 `q`，且维度分别是 $(3 n_\\mathrm{Atom}, 3 n_\\mathrm{Atom})$ 与 $(3 n_\\mathrm{Atom},)$。注意到 `e` 的单位是 E<sub>h</sub> Bohr<sup>-2</sup> amu<sup>-1</sup>，而 `q` 现在是无量纲量。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "e, q = np.linalg.eigh(theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "现在获得的原始分子频率事实上是力常数除以质量的结果，或者按照 Levine (7ed) p63, eq (4.23) 的表达，为 $k/m$。因此，化为以波数表示的频率 `freq_cm_1` 的公式是\n",
    "\n",
    "$$\n",
    "\\tilde \\nu = \\frac{1}{2 \\pi c_0} \\sqrt{\\frac{k}{m}}\n",
    "$$\n",
    "\n",
    "其中，$c_0$ 表示真空光速。在实行具体计算前，需要将单位转换为国际单位制。最终会将频率转成 cm<sup>-1</sup> 单位。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-3561.40505, -2816.91767,  -168.16445,  -156.49378,  -118.3671 ,    -0.05708,     0.00635,     0.02696,    43.3215 ,   289.57484,   359.82004,\n",
       "         542.70646,   584.63229,   646.04288,   680.41788,   775.32894,  1115.58713,  1346.89468,  1521.52455,  1593.04881,  1969.81362])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "freq_cm_1 = np.sqrt(np.abs(e * E_h * 1000 * N_A / a_0**2)) / (2 * np.pi * c_0 * 100) * ((e > 0) * 2 - 1)\n",
    "freq_cm_1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "需要留意，复数的频率实际上是虚数频率，或者说是现实中不存在的频率；使用复数表示这些频率仅仅是为了程序方便，以及约定俗称的原因。\n",
    "\n",
    "由于分子的振动自由度 (对于非线性分子) 是 $3 n_\\mathrm{Atom} - 6$，因此其中有 6 个频率不应当归属于振动频率中。大多数情况下，舍去绝对值最小的六个频率即可；但其值仍然会与 Gaussian 给出的结果有少许的不同。\n",
    "\n",
    "简正坐标在这里我们暂时不进行更多说明；在叙述去除平动、转动的频率后，我们再讨论简正坐标的导出。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 去除平动、转动的频率"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "去除平动、转动对频率的贡献，其过程大致是预先将平动、转动的模式求取，随后将力常数张量投影到平动、转动模式的补空间 ($3 n_\\mathrm{Atom} - 6$ 维度空间)，得到新的力常数张量。\n",
    "\n",
    "其中的大部分内容应当在 Wilson et al. [^Wilson-Cross.Dover.1980] 的 Chapter 2 可以找到。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 质心坐标"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`center_coord` $C_t$ 表示质心坐标，维度 $(3,)$，单位 Bohr。\n",
    "\n",
    "$$\n",
    "C_{t} = \\frac{\\sum_{A} A_{t} w_A}{\\sum_A w_A}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.56385, -0.44307, -0.07436])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "center_coord = (mol_coord * mol_weight[:, None]).sum(axis=0) / mol_weight.sum()\n",
    "center_coord"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`centered_coord` $A^\\mathrm{C}_t$ 是将质心平移至原点后的原子坐标，维度 $(n_\\mathrm{Atom}, 3)$，单位 Bohr。\n",
    "\n",
    "$$\n",
    "A^\\mathrm{C}_t = A_t - C_t\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "centered_coord = mol_coord - center_coord"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 转动惯量本征向量"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`rot_tmp` $I_{ts}$ 是转动惯量相关的矩阵，在初始化时维度为 $(n_\\mathrm{Atom}, 3, 3)$，最终结果通过求和得到 $(3, 3)$ 的矩阵，单位 Bohr<sup>2</sup> amu。\n",
    "\n",
    "$$\n",
    "\\begin{split}\n",
    "I_{ts} =\n",
    "\\begin{cases}\n",
    "    \\sum_{A} w_A \\left( - (A_t^\\mathrm{C})^2 + \\sum_r (A_r^\\mathrm{C})^2 \\right) \\,, & t = s \\\\\n",
    "    \\sum_{A} w_A \\left( - A_t^\\mathrm{C} A_s^\\mathrm{C} \\right) \\,, & t \\neq s\n",
    "\\end{cases}\n",
    "\\end{split}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "rot_tmp = np.zeros((natm, 3, 3))\n",
    "rot_tmp[:, 0, 0] = centered_coord[:, 1]**2 + centered_coord[:, 2]**2\n",
    "rot_tmp[:, 1, 1] = centered_coord[:, 2]**2 + centered_coord[:, 0]**2\n",
    "rot_tmp[:, 2, 2] = centered_coord[:, 0]**2 + centered_coord[:, 1]**2\n",
    "rot_tmp[:, 0, 1] = rot_tmp[:, 1, 0] = - centered_coord[:, 0] * centered_coord[:, 1]\n",
    "rot_tmp[:, 1, 2] = rot_tmp[:, 2, 1] = - centered_coord[:, 1] * centered_coord[:, 2]\n",
    "rot_tmp[:, 2, 0] = rot_tmp[:, 0, 2] = - centered_coord[:, 2] * centered_coord[:, 0]\n",
    "rot_tmp = (rot_tmp * mol_weight[:, None, None]).sum(axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`rot_eig` $R_{ts}$ 是转动惯量相关的对称矩阵 $I_{ts}$ 所求得的本征向量，维度 $(3, 3)$，无量纲。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.80658, -0.54971,  0.21739],\n",
       "       [-0.16056, -0.55765, -0.8144 ],\n",
       "       [ 0.56891,  0.62197, -0.53805]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "_, rot_eig = np.linalg.eigh(rot_tmp)\n",
    "rot_eig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 平动、转动投影矩阵"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`proj_scr` $P_{A_t q}$ 是平动、转动的 $(3 n_\\mathrm{Atom}, 6)$ 维度投影矩阵，其目的是将 $\\Theta^{A_t B_s}$ 中不应对分子振动产生贡献的部分投影消去，剩余的 $3 n_\\mathrm{Atom} - 6$ 子空间用于求取实际的分子振动频率。但在初始化 `proj_scr` $P_{A_t q}$ 时，先使用 $(n_\\mathrm{Atom}, 3, 6)$ 维度的张量。\n",
    "\n",
    "在计算投影矩阵前，我们先生成 `rot_coord` $\\mathscr{R}_{Asrw}$ 转动投影相关量，维度 $(n_\\mathrm{Atom}, 3, 3, 3)$：\n",
    "\n",
    "$$\n",
    "\\mathscr{R}_{Asrw} = \\sum_{t} A^\\mathrm{C}_t R_{ts} R_{rw}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(7, 3, 3, 3)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rot_coord = np.einsum(\"At, ts, rw -> Asrw\", centered_coord, rot_eig, rot_eig)\n",
    "rot_coord.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "随后我们给出 `proj_scr` 的计算表达式。`proj_scr` 的前三列表示平动投影，当 $q \\in (x, y, z) = (0, 1, 2)$ 时，\n",
    "\n",
    "$$\n",
    "P_{A_t q} = \\sqrt{w_A} \\delta_{tq}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "而当 $q \\in (x, y, z) = (3, 4, 5)$ 时，\n",
    "\n",
    "$$\n",
    "\\begin{split}\n",
    "P_{A_t q} = \\sqrt{w_A} \\times\n",
    "\\begin{cases}\n",
    "    \\mathscr{R}_{Aytz} - \\mathscr{R}_{Azty} \\,, & q = x \\\\\n",
    "    \\mathscr{R}_{Aztx} - \\mathscr{R}_{Axtz} \\,, & q = y \\\\\n",
    "    \\mathscr{R}_{Axty} - \\mathscr{R}_{Aytx} \\,, & q = z\n",
    "\\end{cases}\n",
    "\\end{split}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "最终，我们会将 $P_{A_t q}$ 中关于 $A_t$ 的维度进行归一化，因此最终获得的 $P_{A_t q}$ 是无量纲的。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.36722,  0.     ,  0.     ,  0.00369,  0.05794,  0.11255],\n",
       "       [ 0.     ,  0.36722,  0.     ,  0.04243, -0.17071,  0.09139],\n",
       "       [ 0.     ,  0.     ,  0.36722,  0.00675, -0.10185, -0.09286],\n",
       "       [ 0.42396,  0.     ,  0.     ,  0.01229, -0.02015, -0.0705 ],\n",
       "       [ 0.     ,  0.42396,  0.     , -0.49194, -0.29189,  0.22557],\n",
       "       [ 0.     ,  0.     ,  0.42396, -0.15626, -0.27952, -0.36992],\n",
       "       [ 0.36722,  0.     ,  0.     ,  0.03114,  0.00301, -0.06566],\n",
       "       [ 0.     ,  0.36722,  0.     ,  0.11694,  0.18118, -0.11688],\n",
       "       [ 0.     ,  0.     ,  0.36722, -0.01115,  0.16511,  0.15039],\n",
       "       [ 0.42396,  0.     ,  0.     ,  0.16731, -0.02119, -0.43088],\n",
       "       [ 0.     ,  0.42396,  0.     , -0.30661,  0.34319, -0.15655],\n",
       "       [ 0.     ,  0.     ,  0.42396, -0.32374,  0.28897,  0.06287],\n",
       "       [ 0.42396,  0.     ,  0.     , -0.02565,  0.18716,  0.45037],\n",
       "       [ 0.     ,  0.42396,  0.     ,  0.3913 , -0.45793,  0.21108],\n",
       "       [ 0.     ,  0.     ,  0.42396,  0.1468 , -0.24516, -0.13753],\n",
       "       [ 0.42396,  0.     ,  0.     , -0.19609, -0.19816,  0.03903],\n",
       "       [ 0.     ,  0.42396,  0.     ,  0.31205,  0.3942 , -0.26137],\n",
       "       [ 0.     ,  0.     ,  0.42396,  0.36608,  0.17829,  0.41139],\n",
       "       [ 0.10642,  0.     ,  0.     ,  0.04773, -0.00179, -0.11404],\n",
       "       [ 0.     ,  0.10642,  0.     , -0.17067,  0.01343,  0.01336],\n",
       "       [ 0.     ,  0.     ,  0.10642, -0.11584,  0.01045, -0.06629]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "proj_scr = np.zeros((natm, 3, 6))\n",
    "proj_scr[:, (0, 1, 2), (0, 1, 2)] = 1\n",
    "proj_scr[:, :, 3] = (rot_coord[:, 1, :, 2] - rot_coord[:, 2, :, 1])\n",
    "proj_scr[:, :, 4] = (rot_coord[:, 2, :, 0] - rot_coord[:, 0, :, 2])\n",
    "proj_scr[:, :, 5] = (rot_coord[:, 0, :, 1] - rot_coord[:, 1, :, 0])\n",
    "proj_scr *= np.sqrt(mol_weight)[:, None, None]\n",
    "proj_scr.shape = (-1, 6)\n",
    "proj_scr /= np.linalg.norm(proj_scr, axis=0)\n",
    "proj_scr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "最后我们声明，在经过上述投影后的力常数矩阵几乎表现为零：\n",
    "\n",
    "$$\n",
    "\\mathbf{P}^\\dagger \\mathbf{\\Theta} \\mathbf{P} \\simeq \\mathbf{0}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.     ,  0.     ,  0.     , -0.     , -0.     ,  0.     ],\n",
       "       [ 0.     ,  0.     ,  0.     , -0.     , -0.     , -0.     ],\n",
       "       [ 0.     ,  0.     ,  0.     ,  0.     ,  0.     ,  0.     ],\n",
       "       [-0.     , -0.     ,  0.     , -0.00034,  0.00053, -0.00012],\n",
       "       [-0.     , -0.     ,  0.     ,  0.00053,  0.00001,  0.00011],\n",
       "       [ 0.     , -0.     ,  0.     , -0.00012,  0.00011, -0.00021]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "proj_scr.T @ theta @ proj_scr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "对上述矩阵进行对角化所给出的平动、转动频率如下："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-142.94819,  -65.35067,   -0.05708,    0.00635,    0.02696,  102.63548])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e_tr, _ = np.linalg.eigh(proj_scr.T @ theta @ proj_scr)\n",
    "np.sqrt(np.abs(e_tr * E_h * 1000 * N_A / a_0**2)) / (2 * np.pi * c_0 * 100) * ((e_tr > 0) * 2 - 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "scrolled": false
   },
   "source": [
    "### 平动、转动投影矩阵的补空间"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "既然我们已经得到了平动、转动的投影，那么根据矩阵的原理，相应地我们也能获得其补空间的投影。我们令 `proj_inv` $Q_{A_t q}$ 为 $P_{A_t q}$ 的补空间投影。获得补空间的大致方式是预先定义一个仅有一个分量为 $1$ 的 $(3 n_\\mathrm{Atom}, )$ 维度向量，随后通过 Schmit 正交的方式给出已有投影空间的补空间向量。组合这些 Schmit 正交的向量便获得了 $Q_{A_t q}$。\n",
    "\n",
    "$Q_{A_t q}$ 的维度本应当是 $(3 n_\\mathrm{Atom}, 3 n_\\mathrm{Atom} - 6)$ 维。但为了程序编写方便，我们先规定 `proj_inv` 是 $(3 n_\\mathrm{Atom}, 3 n_\\mathrm{Atom})$ 维度，并且其中的前 6 列填入 $P_{A_t q}$；在进行 Schmit 正交化后，再将前 6 列剔除。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "proj_inv = np.zeros((natm * 3, natm * 3))\n",
    "proj_inv[:, :6] = proj_scr\n",
    "cur = 6\n",
    "for i in range(0, natm * 3):\n",
    "    vec_i = np.einsum(\"Ai, i -> A\", proj_inv[:, :cur], proj_inv[i, :cur])\n",
    "    vec_i[i] -= 1\n",
    "    if np.linalg.norm(vec_i) > 1e-8:\n",
    "        proj_inv[:, cur] = vec_i / np.linalg.norm(vec_i)\n",
    "        cur += 1\n",
    "    if cur >= natm * 3:\n",
    "        break\n",
    "proj_inv = proj_inv[:, 6:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们最后获得的 $Q_{A_t q}$ 是列正交切归一的矩阵，且形式大致是下三角矩阵。但需要留意，对于当前的分子，最后一列只有 6 个非零值，与倒数第二列非零值的数量相差 2 个。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.92147, -0.     ,  0.     , -0.     , -0.     ,  0.     , -0.     , -0.     ],\n",
       "       [ 0.0006 , -0.90876,  0.     ,  0.     ,  0.     , -0.     ,  0.     , -0.     ],\n",
       "       [-0.01772,  0.0101 , -0.91962,  0.     ,  0.     ,  0.     ,  0.     , -0.     ],\n",
       "       [ 0.15913, -0.00263,  0.00635, -0.88846,  0.     ,  0.     , -0.     , -0.     ],\n",
       "       [ 0.00723,  0.22587,  0.00828, -0.0174 , -0.62508, -0.     ,  0.     ,  0.     ],\n",
       "       [-0.06338,  0.00797,  0.23777,  0.02386,  0.12464, -0.71004, -0.     ,  0.     ],\n",
       "       [ 0.13864, -0.00562,  0.00379,  0.20568, -0.05571,  0.01213, -0.89165, -0.     ],\n",
       "       [-0.00242,  0.10806, -0.00617,  0.00599,  0.06901, -0.02449,  0.00896, -0.88757],\n",
       "       [ 0.02871, -0.01639,  0.11235, -0.00984, -0.01789,  0.10978, -0.00552,  0.00503],\n",
       "       [ 0.11566, -0.03146,  0.04451,  0.26042, -0.29396,  0.15738,  0.31106,  0.0477 ],\n",
       "       [ 0.00123,  0.07679, -0.02363,  0.00022,  0.33955,  0.06639, -0.01868,  0.25957],\n",
       "       [ 0.02455, -0.06306,  0.1274 , -0.01053,  0.12201,  0.23871, -0.01701,  0.00208],\n",
       "       [ 0.23563,  0.00909, -0.07083,  0.20364,  0.09472, -0.32385,  0.2141 , -0.00369],\n",
       "       [-0.00144,  0.29684,  0.03556, -0.00183,  0.37737,  0.06574, -0.02848,  0.16881],\n",
       "       [-0.03163,  0.03906,  0.21245,  0.01424, -0.03451,  0.45782,  0.02184, -0.02423],\n",
       "       [ 0.16048,  0.0321 ,  0.01383,  0.22974,  0.26819,  0.14629,  0.22725, -0.04739],\n",
       "       [-0.00589,  0.08555, -0.01393,  0.01471, -0.20618, -0.12656,  0.04452,  0.32995],\n",
       "       [ 0.06292,  0.02501,  0.10976, -0.01965, -0.21114, -0.11824,  0.00024,  0.01928],\n",
       "       [ 0.02856, -0.00888,  0.01142,  0.06576, -0.08244,  0.03852,  0.07928,  0.01347],\n",
       "       [ 0.00179,  0.03386, -0.00375, -0.00353,  0.21735,  0.06231, -0.0204 ,  0.04162],\n",
       "       [-0.0079 , -0.01404,  0.04718,  0.00238,  0.05775,  0.14602, -0.00114, -0.00595]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "proj_inv[:, :8]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.     , -0.     ,  0.     ,  0.     , -0.     ,  0.     , -0.     ],\n",
       "       [ 0.     , -0.     ,  0.     ,  0.     ,  0.     , -0.     , -0.     ],\n",
       "       [ 0.     ,  0.     , -0.     ,  0.     , -0.     , -0.     , -0.     ],\n",
       "       [ 0.     ,  0.     , -0.     , -0.     ,  0.     , -0.     ,  0.     ],\n",
       "       [-0.     ,  0.     ,  0.     ,  0.     ,  0.     ,  0.     ,  0.     ],\n",
       "       [-0.     , -0.     , -0.     , -0.     ,  0.     ,  0.     , -0.     ],\n",
       "       [ 0.     , -0.     ,  0.     ,  0.     , -0.     ,  0.     , -0.     ],\n",
       "       [-0.     , -0.     , -0.     , -0.     , -0.     , -0.     , -0.     ],\n",
       "       [-0.88821,  0.     , -0.     , -0.     , -0.     ,  0.     ,  0.     ],\n",
       "       [-0.04822, -0.55628,  0.     ,  0.     , -0.     ,  0.     , -0.     ],\n",
       "       [ 0.03972, -0.14218, -0.60686, -0.     , -0.     ,  0.     , -0.     ],\n",
       "       [ 0.28906, -0.17446,  0.45345, -0.46401, -0.     ,  0.     ,  0.     ],\n",
       "       [ 0.06431,  0.06973,  0.00436,  0.05117, -0.55525,  0.     , -0.     ],\n",
       "       [-0.05364, -0.22108,  0.16095, -0.21835, -0.04109, -0.14297, -0.     ],\n",
       "       [ 0.18656,  0.31662, -0.22295,  0.16951, -0.42471,  0.25709,  0.     ],\n",
       "       [-0.01297,  0.40547,  0.02383,  0.0214 ,  0.5487 ,  0.10936, -0.18819],\n",
       "       [ 0.01152,  0.40633,  0.35634,  0.05943,  0.02677,  0.08518, -0.13536],\n",
       "       [ 0.27891, -0.14836, -0.26106,  0.18737,  0.44457, -0.05496,  0.07441],\n",
       "       [-0.01243,  0.32303, -0.11228, -0.28913,  0.02613, -0.43568,  0.74973],\n",
       "       [ 0.00958, -0.17158,  0.35684,  0.63313,  0.05705,  0.23023,  0.53923],\n",
       "       [ 0.05897,  0.02469,  0.12176,  0.42675, -0.07912, -0.80524, -0.29643]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "proj_inv[:, 8:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 去除平动、转动部分的频率"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们将对矩阵 $\\mathbf{Q}^\\dagger \\mathbf{\\Theta} \\mathbf{Q}$ 进行对角化；且获得的第 $q$ 个简正坐标的频率相关量 `e` $K_q = k_q / m_q$ 与原始简正坐标 `q` $\\mathbf{q}^\\mathrm{orig}$ 表示如下：\n",
    "\n",
    "$$\n",
    "\\mathbf{Q}^\\dagger \\mathbf{\\Theta} \\mathbf{Q} \\mathbf{q}^\\mathrm{orig} = \\mathbf{q}^\\mathrm{orig} \\mathrm{diag} (\\boldsymbol{K})\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "e, q = np.linalg.eigh(proj_inv.T @ theta @ proj_inv)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "由此，我们就可以立即获得去除平动、转动部分的，以 cm<sup>-1</sup> 为单位的，总数为 $3 n_\\mathrm{Atom} - 6$ 的分子频率 `freq_cm_1`："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-3561.40117, -2816.7847 ,  -111.10727,   285.51964,   354.79005,   541.46285,   583.67422,   641.59573,   678.70706,   774.75315,  1114.8334 ,\n",
       "        1341.17965,  1521.15243,  1592.00939,  1969.72731])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "freq_cm_1 = np.sqrt(np.abs(e * E_h * 1000 * N_A / a_0**2)) / (2 * np.pi * c_0 * 100) * ((e > 0) * 2 - 1)\n",
    "freq_cm_1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 归一化的简正坐标"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "方才通过对角化，我们获得的原始简正坐标 `q` 的维度是 $3 n_\\mathrm{Atom} - 6$。我们需要通过 `q` $\\mathbf{q}^\\mathrm{orig}$ 重塑回正常的简正坐标的维度 $q_{A_t q}$ $(3 n_\\mathrm{Atom}, 3 n_\\mathrm{Atom} - 6)$。\n",
    "\n",
    "我们首先给出未经过归一化的简正坐标，命名为 `q_unnormed` $q_{A_t q}^\\mathrm{unnorm}$，其单位是 amu<sup>-1/2</sup>。该量将会用于后续的红外强度计算上。其计算过程大致是\n",
    "\n",
    "$$\n",
    "\\mathbf{q}^\\mathrm{unnorm} = \\mathbf{Q} \\mathbf{q}^\\mathrm{orig} / \\sqrt{\\mathbf{w}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "q_unnormed = np.einsum(\"AtQ, A -> AtQ\", (proj_inv @ q).reshape(natm, 3, (proj_inv @ q).shape[-1]), 1 / np.sqrt(mol_weight))\n",
    "q_unnormed = q_unnormed.reshape(-1, q_unnormed.shape[-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "而将每一个简正坐标的振动强度归一化的矩阵称为 `q_normed` $q_{A_t q}$；它是我们的目标的简正坐标。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "q_normed = q_unnormed / np.linalg.norm(q_unnormed, axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们可以以下述代码核对前三个简正坐标。这些坐标应当与 Gaussian 所输出的坐标几乎相同，或刚好相差正负号。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0.54001, -0.07088, -0.04608],\n",
       "        [-0.14273,  0.02387,  0.00516],\n",
       "        [-0.284  ,  0.09918, -0.24533],\n",
       "        [ 0.03237, -0.03565,  0.07878],\n",
       "        [-0.12144, -0.02845,  0.08535],\n",
       "        [ 0.08194,  0.03046,  0.05426],\n",
       "        [-0.66966, -0.18195, -0.07812]],\n",
       "\n",
       "       [[ 0.0408 , -0.01485,  0.03176],\n",
       "        [-0.02602,  0.02747, -0.02887],\n",
       "        [-0.03581,  0.01862, -0.02587],\n",
       "        [-0.02413, -0.01192,  0.01877],\n",
       "        [-0.01187,  0.00732, -0.02008],\n",
       "        [ 0.0026 , -0.0054 ,  0.00522],\n",
       "        [ 0.88356, -0.32216,  0.32609]],\n",
       "\n",
       "       [[-0.02081,  0.165  ,  0.00726],\n",
       "        [ 0.02702,  0.41713,  0.26319],\n",
       "        [-0.01085,  0.09639, -0.03556],\n",
       "        [ 0.09566, -0.32921, -0.34068],\n",
       "        [ 0.03741, -0.46378, -0.19918],\n",
       "        [-0.13693,  0.19313,  0.30902],\n",
       "        [ 0.00955, -0.21243, -0.17633]]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q_normed.reshape(natm, 3, 3 * natm - 6)[:, :, :3].transpose((2, 0, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 修订记录"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 2021-06-21：重新写了 Schmidt 正交化代码。我不太理解当时的代码到底为什么是对的 (>.<)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[^hess2freq]: <http://sobereva.com/328>\n",
    "\n",
    "[^Wilson-Cross.Dover.1980]: Wilson, E. B.; Decius, J. C.; Cross, P. C. *Molecular Vibrations*; Dover Pub. Inc., 1980."
   ]
  }
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